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In this lesson, we will learn how to determine whether a matrix is symmetric or skew-symmetric and how to use their properties to solve problems.

Q1:

If is a symmetric matrix, what are the values of π₯ , π¦ , and π§ ?

Q2:

Q3:

Which of the following matrices is skew-symmetric?

Q4:

Q5:

Q6:

If π΄ and π΅ are symmetric matrices, does it follow that π΄ π΅ is also symmetric?

Q7:

Given that the matrix is skew-symmetric, find the value of π₯ + π¦ + π§ .

Q8:

Q9:

Q10:

Suppose that π΄ and π΅ are symmetric matrices and that π΄ π΅ = π΅ π΄ . Does it follow that π΄ π΅ is also a symmetric matrix?

Q11:

Find the value of π₯ which makes the following a symmetric matrix.

Q12:

Q13:

Q14:

The non-zero eigenvalues of a real, skew-symmetric matrix are .

Q15:

Which of the following matrices is symmetric?

Q16:

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